The Royals scored five unanswered runs to end Detroit's six-game winning streak.
Butler had two RBI for the Royals and Jacobs had two hits, an RBI and a run scored in the win.
Bruce Chen gave up five runs, seven hits and four walks through 4 2/3 innings.
Yasuhiko Yabuta (1-1) pitched 2 1/3 scoreless frames to earn the win, and Joakim Soria earned his 23rd save of the season.
Ryan Raburn was 3-for-4 with a homer for the Tigers, who maintained their 6 1/2 game lead over Minnesota in the AL Central. Marcus Thames and Aubrey Huff each drove in two of runs in defeat.
Rick Porcello started and allowed four runs and seven hits in six innings. Bobby Seay (5-3) took the loss after yielding two runs in two-thirds of an inning.